Question

what is a solution to (x + 6)(x + 2) = 60?
x = -6
x = -4
x = 4
x = 12

Explanation:

Step1: Expand the left side

Using the distributive property (FOIL method), \((x + 6)(x + 2)=x^2+2x + 6x+12=x^2 + 8x+12\). So the equation becomes \(x^2+8x + 12=60\).

Step2: Rearrange to standard quadratic form

Subtract 60 from both sides: \(x^2+8x+12 - 60=0\), which simplifies to \(x^2+8x - 48=0\). Alternatively, we can test each option by substituting into the original equation.

Testing \(x = - 6\):

Substitute \(x=-6\) into \((x + 6)(x + 2)\): \((-6 + 6)(-6+2)=(0)(-4)=0
eq60\). So \(x = - 6\) is not a solution.

Testing \(x=-4\):

Substitute \(x = - 4\) into \((x + 6)(x + 2)\): \((-4 + 6)(-4+2)=(2)(-2)=-4
eq60\). So \(x=-4\) is not a solution.

Testing \(x = 4\):

Substitute \(x = 4\) into \((x + 6)(x + 2)\): \((4 + 6)(4+2)=(10)(6)=60\). This satisfies the equation.

Testing \(x = 12\):

Substitute \(x = 12\) into \((x + 6)(x + 2)\): \((12 + 6)(12+2)=(18)(14)=252
eq60\). So \(x = 12\) is not a solution.

Answer:

C. \(x = 4\) (assuming the options are labeled as A. \(x=-6\), B. \(x = - 4\), C. \(x = 4\), D. \(x = 12\))